Consider the situation shown in figure. We find electric field $E$ at point $P$ using Gauss's law and it comes out to be $E=\frac{\sigma }{{\epsilon }_0}$. This electric field is due to

A cavity of radius $r$ is made inside a solid sphere. The volume charge density of the remaining sphere is $\rho$. An electron (charge $e$, mass $m$) is released inside the cavity from point $P$ as shown in the figure. The centre of sphere and the centre of the cavity arc is separated by a distance $a$. The time after which the electron again touches the sphere is